The Hausdorff dimension of the set of dissipative points for a Cantor-like model set for singly cusped parabolic dynamics
Schmeling, Jörg ; Stratmann, Bernd O.
Kodai Math. J., Tome 32 (2009) no. 1, p. 179-196 / Harvested from Project Euclid
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In this paper we introduce and study a certain intricate Cantor-like set $\mathcal{C}$ contained in unit interval. Our main result is to show that the set $\mathcal{C}$ itself, as well as the set of dissipative points within $\mathcal{C}$ , both have Hausdorff dimension equal to 1. The proof uses the transience of a certain non-symmetric Cauchy-type random walk.
Publié le : 2009-06-15
Classification:  
@article{1245982902,
     author = {Schmeling, J\"org and Stratmann, Bernd O.},
     title = {The Hausdorff dimension of the set of dissipative points for a Cantor-like model set for singly cusped parabolic dynamics},
     journal = {Kodai Math. J.},
     volume = {32},
     number = {1},
     year = {2009},
     pages = { 179-196},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1245982902}
}

Schmeling, Jörg; Stratmann, Bernd O. The Hausdorff dimension of the set of dissipative points for a Cantor-like model set for singly cusped parabolic dynamics. Kodai Math. J., Tome 32 (2009) no. 1, pp.  179-196. http://gdmltest.u-ga.fr/item/1245982902/